Primality proof for n = 20187911:

Take b = 2.

b^(n-1) mod n = 1.

42953 is prime.
b^((n-1)/42953)-1 mod n = 4757465, which is a unit, inverse 10221519.

(42953) divides n-1.

(42953)^2 > n.

n is prime by Pocklington's theorem.